Here's the location, copied from http://support.apple.com/kb/TS3694 Advanced section:
Rename, move, or delete the iOS software file (.ipsw)
iTunes uses "ipsw" files to restore your iPod or iPhone. If those files are unusable, then try deleting them, renaming them, or moving the file to a different directory. This will cause iTunes to download a new copy of the IPSW. When a restore issue is specific to a user, it is likely due to an unusable .ipsw file. If removing the .ipsw file does not resolve a user-specific restore issue, then the issue is caused by other user-specific security software settings or iTunes preferences. Creating a new user will also cause new .ipsw restore files to be downloaded in the new user. You can find the ".ipsw" files in these locations:
Mac OS X
~/Library/iTunes/iPhone Software Updates
~/Library/iTunes/iPad Software Updates
~/Library/iTunes/iPod Software Updates
Note: The tilde "~" represents your Home directory.
I found and deleted the .ispw files, tried to download the software again, but still no. It gives me the message when I try to sync apps that I need newer software, and when I check for updates it says I have the latest.
I tried the other option by creating a new user, but same results.
Also, after I have downloaded the update, it does not show in the path to the .ispw files - is that right?
A 1G iPod can only go to iOS 3.1.3. There are presently few apps available in the App store that will work with iOS 3.1.3. Most now require iOS 4 or later. When developers have been updating their apps for iOS 5 most seem to be dropping support for iOS 3 and earlier. SInce you can only purchased the latest version for the Apps store, unless you already purchased and have the earlier version you are out of luck.